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Full text of "Logarithmically periodic resonant-v arrays"




LI BRAHY 

OF THE 

U N IVER.SITY 

Of ILLI NOIS 

621.365 

Ii655-te 

no. 40-49 

cop. 2 



Digitized by the Internet Archive 
in 2013 



http://archive.org/details/logarithmicallyp47maye 



ANTENNA LABORATORY 
Technical Report No. 47 

LOGARITHMICALLY PERIODIC RESONANT-V ARRAYS 

by 
Paul E. Mayes and Robert L. Carrel 

15 July 1960 



Contract AF33 (616) -6079 
Project No. 9-(13-6278) Task 40572 



Sponsored by: 
WRIGHT AIR DEVELOPMENT CENTER 



Electrical Engineering Research Laboratory 

Engineering Experiment Station 

University of Illinois 



Urbana, Illinois 



4»=> 

.ENGINEERIjMu l 

CONTENTS 

Page 

1. Introduction 1 

2. Development of the Log-Periodic Resonant-V Array 3 

2.1 Log-Periodic Design Principles 3 

2.1.1 Similitude 3 

2„1.2 Truncation 3 

2.1,3 The Active Region 5 

2.2 The Log-Periodic Dipole Array 5 

2.2.1 Description 5 

2.2.2 Results 5 

2.3 Theory of Higher Order Resonant Modes 7 

3. Experimental Results 11 

3.1 Pattern Measurements 11 

3.1.1 Construction of the Pattern Models 11 

3.1.2 General Pattern Measurement Results and Interpreta- 
tions 14 

3.1.3 Radiation Patterns and the Variation of 4 1 16 

3.1.4 Radiation Patterns and Directivity Data 19 

3.1.5 Minimum Array Length and Maximum Element Spacing 30 

3.2 Impedance Measurements 32 

3.2.1 Construction of the Impedance Models 32 

3.2.2 Description of the Measurements and the Measuring 
Equipment 34 

3.2.3 General Results of the Measurements of Impedance on 

LP Structures 36 

3.2.4 Input Impedance: Single Mode Operation 38 

3.2.5 Input Impedance: Multi-Mode Operation 38 

3,2.5.1 Determination of the Weighted Mean 

Resistance Level R 38 

3.2.5„2 R Tir „, as a Function of LPVA Parameters 42 

WM 

4. Design Considerations for Particular Applications 46 

4.1 Elimination of Central Elements 46 

4.2 Off -Axis Beams 46 

3. Conclusions 55 

References 56 



1. INTRODUCTION 



The principle of logarithmic periodicity has become well-established 

in the design of frequency independent antennas. The first log-periodic 

1 2 

antennas had moderate directive gain. Like the logarithmic spiral 

antennas, however, the log-periodic structures were unusual because they 
maintained nearly the same value of gain over arbitrary frequency bands. 

In order to achieve higher gains log-periodic antennas have been used in 

3 4 
arrays and as feeds for reflectors and lenses ' . The purpose of this 

paper is to show that higher gains are also obtainable with operation of 

LP antennas in higher order modes. 

The log-periodic principles have recently been applied to the design 

5 
of a frequency independent array of dipoles . By proper choice of design 

parameters, the log-periodic dipole array with a length of the order of 

one wavelength at the lowest frequency can be made to yield a directive 

gain of 10 db (compared to an isotropic radiator) over a 2:1 bandwidth. 

Lower gains can be achieved over much wider bandwidths. The pattern and 

impedance are essentially independent of frequency over a bandwidth which 

is governed by the size of the structure and the precision of construction. 

The directivity of the log-peridoic dipole array is achieved from 
both the directive element pattern of the half wave dipoles and the 
directive array factor of an end-fire array. The directivity can be 
increased by replacing the half-wave dipoles with more directive resonant-V 
elements. To obtain the increased directivity of the V elements it is 
necessary to operate the elements at higher odd-half -wavelength resonances. 
Directive gains in excess of 15 db over isotropic can be achieved when 
operating the array in the higher modes. The same structure can be used 
in several modes to achieve coverage of different frequency bands. An 
efficient utilization of the structure is obtained in this way, since 
many of the elements will be used at more than one frequency, 

Typical directive gains from 12 db (over isotropic) in the three- 
half-wavelengths mode to 17 db in the seven-half -wavelengths mode have 
been obtained. The input impedance can be controlled to some extent by 
choice of design parameters. A VSWR less than 3:1 can be achieved across 



the entire band covered by several modes except at "transition" regions 
where operation changes from one mode to another. 



2. DEVELOPMENT OF THE LOG-PERIODIC RESONANT-V ARRAY 

2 .1. Log-Periodic Design Principles 

2.1ol Similitude 

The idea in log-peridoic antenna design is to use the principle of 
similitude in the design of interconnected "cells" of the antenna. Each 
cell is exactly like the adjacent cell except for a scale factor, T . 
Such a connected group of cells is shown schematically in Figure 1. If 
the number of cells is unlimited, the entire structure will transform into 
itself when scaled by T or any integer power of T . It is assumed that the 
structure is built from very good conductors so that the effect of finite 
conductivity can be neglected in the application of similitude. 

If the method used to excite the structure is independent of frequency, 
the electromagnetic performance must be the same (except for a change in 
scale) at all frequencies related by T (n integer) . This frequency independent 
requirement on the excitation dictates that the source be placed at the 
small end of the structure. 

Each band of frequencies between any f and Tf corresponds to one period 
of the structure. In order to be frequency independent (or nearly so) the 
variation in performance across a frequency period must be negligible. 
Not all log-periodic structures are frequency independent antennas. There 
are a number of log-periodic structures, however, which, for a limited 
range of parameters, do display only a small variation in performance over 
a period. 

2.1.2 Truncation 

In any physical structure it is possible to duplicate the conditions 
outlined above only for a finite (relatively small) number of cells. Since 
each successive cell must be increasingly larger, it is inevitable that one 
must reach a practical limit as to size. Going in the other direction, 
there is a limit to the precision with which one can construct the very 
small cells. Therefore, it is necessary to truncate the idealized infinite 
bandwidth structure to form a practical antenna. If at some frequency 
most of the energy is radiated from a limited number of cells of the 
structure, then it is possible that the portion of the structure beyond 
the radiating section will be unexcited and its presence or absence makes 






(n*3) 
cell 



cell 



(n+l)th 
eel 



W n -i 



■* — L ^i ■» 



Ln + i Wn+i 



rrl 



nth eel 



Ln Wn 



= r 



Wn 



(n-l)th eel 



n 



Figure 1. An Interconnection of a Geometrical Progression of Cells which 
Results in Logarithmically Periodic Performance. 



no difference in the electromagnetic performance at this frequency. In 
this case the fact that the structure has an end rather than extending to 
infinity will not be observable. The troublesome "end effect" of biconical, 
discone and similar antennas is thereby eliminated. 

2.1.3 The Active Region 

From similitude it follows that the radiating portion of the antenna 
must move along the structure as frequency changes. As frequency decreases 
the movement will be towards the large end. Ultimately this "active region" 
will approach the truncation at the large end. When this occurs the antenna 
will cease to function properly. The low frequency limit of the antenna 
bandwidth is thus fixed by the position of the truncation on the large end. 

As frequency increases the active region moves toward the small end. 
At the small end there will be a junction region where the feed is attached 
to the periodic structure. The true periodic geometry can only be carried 
accurately to a certain pointy and beyond this point a transition to the 
feed geometry must occur. When the active region moves into this transition 
as frequency increases once again the antenna performance will deteriorate 
and the high frequency limit on bandwidth will have been reached. 

2.2 The Log-Periodic Dipole Array 

2.2.1 Description 

Isbell found that the log-periodic principles could be applied to 
the design of an array of half-wave dipoles shown schematically in Figure 2. 
To be true to the log-periodic principles the diameter of each element should 
be scaled as well as the length. Also the feed line should be tapered, 
i.e., a conical line. Strict adherence to these requirements is not necessary, 
however, as long as the feed line dimension and element diameters remain 
small in terms of the wavelength over the entire band. In order to obtain 
radiation toward the small end, and thus avoid exciting the larger elements 
beyond the active dipoles, ir radians phase shift was added between adjacent 
elements by effectively "twisting" the feeder. 

2.2.2 Results 



Dipole arrays were found to provide nearly constant patterns and 
impedance over a band of frequencies which could be extended by adding 







*T 



• • • n * a in 



Rn 



In- 

'n-1 



-r 



dn— I 



METHOD OF FEEDING 



■re 2. The Log-Periodic Dipole Array 



more properly-scaled elements to the structure. It was verified that most 
of the energy was radiated from the vicinity of the half-wavelength element. 
With a variation in parameters f, the scaling factor, and a, the angle 
defining the ends of the elments, the following trends were found: 

(a) the directive gain increases as t increases and a decreases 

(b) the average input impedance level decreases with increasing a 
and increasing T . 

It has subsequently been found that the impedance of the feed line 
plays a dominant role in determining the input impedance. It is 
therefore possible to design log-periodic dipole arrays to meet 
directivity and impedance specifications within certain limits. 
Directivities up to 10 db (over isotropic) are easily achieved. Generally 
speaking, high directivity in a log-periodic antenna implies that the active 
region is extended over a number of elements which results in a smaller 
bandwidth than that of an antenna of the same total length but with 
lower directivity. Impedance levels from 55 to 100 ohms were obtained by 
Isbell using a feeder with a characteristic impedance of 105 ohms. 

The dipole array offers considerable advantage over comparable 
parastic (Yagi) arrays in bandwidth and as a result is much less critical 
to adjust for proper operation. 

2.3 Theory of Higher Order Resonant Modes 

In order to achieve high directivity with the log- periodic dipole 
array it is necessary to use long thin arrays (small a) or to use an 
array of two or more dipole arrays. The achievement of satisfactory 
performance of the dipole array at microwave frequencies is difficult 
because small tolerances must be met in construction of the very small 
elements required. The log-periodic array of resonant-V elements offers 
an alternate way to achieve these desirable characteristics of high 
directivity and high frequency performance. 

An array achieves its directivity from both the element pattern and 
the array factor of the elements. The LP dipole array makes effective use 
of the array factor of elements in the active region to achieve end-fire 
directivity. The element pattern, however, is limited to that of the 
half-wave dipoles. A similar array of elements having higher directivity 



8 

'dan T n<- half-wave dipo.e would oe desirable for many applications. Of course, 
the increased directivity would come at the expense of increased element 

size Ln 'erm? if Mveiength. 

V 
The linear d.po L t possesses resonances at n /2 where n is an integer. 

Energy is readily accep T ed from the feeder line of an LP dipole array 

by dipoles which are near any of the odd-integer resonances (n = 1^3, 5., 7, etc .) . 

Thus, if an LP dipole array is operated at a wavelength shorter than twice 

the smallest element length, the energy on the feeder will propagate to 

the \_cinify of rhe three-half -wavelength element and be radiated. The 

elenent patterns of linear dipoles in the higher order resonances are not 

desirable, however, because tney possess multiple lobes as shown in Figure 3. 

When the conductors are bent into the V-shape, however, the pattern has only 

two principal lobes with secondary lobes of small magnitude. The array factor 

ot t r,e LP dipole array has displayed good front-to-back ratio so that the 

oacK*ard lobe of the \ pa f tern wou^d not appear appreciably in the pattern 

oi a log-periodic array of resonant-V elements. 

Since 'he input impedance of linear elements near higher order resonances 

sembles that near the half -wavelength resonance, it would be expected that 

'he input impedance to the array In the higher modes would behave very much 

like r ha' oi the LP dip>it array in the \ 2 mode. 




(a) 3A/2 LINEAR DIPOLE 



Figure 3. E-plane Patterns of Three-Half -Wavelengths 
Linear Dipole and Resonant-V. 









10 









(b) 3A/2 RESONANT- V 

Figure 3b 



11 

3. EXPERIMENTAL RESULTS 

The reasoning outlined in Section 2.3 was tested in June 1959 by constructing 
a small model log-periodic V (LPV) array. The initial results were satisfactory 
and a systematic investigation of LPV antennas with various parameters was 
undertaken. In addition to the parameters in common with the LP dipole array 
the LPV array is described by 4", the angle between the element and the plane 
normal to the feeder. Figure 4 shows the LPV array schematically. 

3.1 Pattern Measurements ^~ 

3.1.1 Construction of the Pattern Models 

The LPV arrays are described by the following parameters (Refer to Figure 4) : 

T - The periodic scaling factor 

h. , h - the half lengths of the longest and shortest elements (-^ = 2h) 

d 

0" = — — — - the spacing to length ratio 
4h 

n 

H 1 - the angle between the plane normal to the array axis and the V elements. 

Z - the characteristic impedance of the feeder 
o 

a/h - radius to half length ratio of elements 

Since a and ^ are not independent parameters in the LPV arrays, the new 
parameter, 0" was defined for these antennas. The parameter 0" gives approximately 
the spacing in wavelengths between elements near the active region in the 

V2 mode c For the n-th mode the spacing in wavelengths near the active region 
is approximately no. When a is used with the LPV arrays in the following 
it will signify the angle which would be subtended by a half element if the 
element were perpendicular to the feeder rather than bent to form a V. 
In this sense the parameter a can be used to compare LP dipole and LPV 
arrays. Given a and T^ Q can be determined from the formula 

a = \ E 1 -* 1 *] cot a CD 

A nomograph of this relationship is given in Figure 5, 

Several small models of LPV arrays have been constructed for radiation 
pattern measurements. Coin silver tubing (0.125 in c and 0.148 in. diameter) 
vas used for the feeder conductors and copper wire (0.05 in. diameter) was 



12 



DIRECTION OF BEAM MAXIMUM 



FEEDER(described by Z n ) 




Figure 4. The Log-Periodic Resonant-V Array 



13 





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NOMOGRAPH OF 

0*" — (I -a) cot or 
4 

Figure 5 



14 



used for the elements. These antennas are fed with a coaxial cable in the 

5 

same manner as the LP dipole arrays. A microdot cable is threaded from 

rear to front through one of the hollow feeder conductors. The outer 
conductor of the cable is connected to one feeder conductor; the center 
conductor to the other. A frequency independent conversion from unbalanced 
to balanced line is made at the antenna feed point because of the manner in 
which the current diminishes along the structure due to radiation. 

Because the feeder line usually carries negligible current past the 
active region, the termination of this line is relatively unimportant. 
For uniformity in the results and to provide mechanical support, a shprt 
circuit termination located a distance 1/2 h. behind the longest element was 
used in all the pattern models. The models tested and their parameters 
are listed in Table 1„ A photograph of LPV - 8 is shown in Figure 6. 

TABLE 1 



Model No. 


N 


LPV-1 


20 


LPV-2 


25 


LPV-3 


25 


LPV-4 


12 


LPV-5 


12 


LPV-6 


12 


LPV-7 


14 


LPV-8 


14 


LPV-9 


11 



0.95 

0.95 

0.95 

0.888 

0.888 

0.888 

0.91 

0.91 

0.888 



(J 

0.0461 

0.0694 

0.0268 

0.112 

0.0444 

0.025 

0.0257 

0.053 

0.066 



^(Degrees) 



0,32.5,40,45,50 



0,45, 


50, 


55 


0,45, 


50, 


55 


0,45, 


50 




45,55 






45,55 






55 






55 






55 







Number of elements. 

3.1.2 General Pattern Measurement Results and Interpretations 
Radiation patterns were taken, starting at a frequency f near the 
low Lmit, at frequencies T~ P f ( p = integer or integer plus 

1/2) until ih" high frequency bandlimil (or the upper frequency limit of the 
pattern range eq I countered, 

the firel models tested were good over most of the band 
At some spots Ln the band, however, Lobing or the patterns was observed and 
acf ' larg( croee-polarization component. It is to be 

hi occur a1 the "transition" frequencies 



15 




Figure 6. The Pattern Model of LPV-8 . 



16 

between modes. 

At the low frequency bandlimit the active region is located near a 
half-wavelength element at the rear of the structure. As frequency increases 
the active region moves toward the front of the antenna. Since the array 
is truncated on the front end also, a frequency will be reached at which 
there are no half-wave elements on the structure. If the ratio of largest 
to smallest element length exceeds 3, there will be a three-half-wavelength 
element at this frequency. There will be a band of frequencies, however, 
in which radiation will occur from the front elements, even though somewhat 
shorter than V2, as well as the 3^/2 elements toward the rear. When these 
two active regions radiate simultaneously from positions which are separated 
by distances of the order of the wavelength, the path difference between 
the two regions would be sufficient to cause lobing of the patterns. 

It is likely, too, that the input impedance in the transition band would 
not be good, resulting in a smaller amount of radiation of the principlal 
polarization from the antenna. This would account for the higher relative 
level of the always present cross-polarized field. It was indeed found that 
most of the frequencies where lobing or other significant changes in pattern 
shape occurred could be included in the transition bands between various 
modes. 

It was also found that the cross-polarized radiation could be reduced 
considerably by taking greater care in the construction. Figure 7 shows 
three types of construction that were used on one model (LPV-3) in order to 
compare performance. The construction shown in (c) was found to be superior 
to the others, displaying considerably lower cross-polarization and fewer 
pattern anomalies. A close-up photograph in Figure 8 further illustrates 
this method of bending the elements so that they all lie in the same plane. 

3.1.3 Radiation Patterns and the Variation of ^ 

The radiation pattern of the V elements depends upon the angle of the 

7 
V. For <ach mode there is a different angle which produces maximum gain. 



17 




FEED CONDUCTORS 



ANTENNA ELEMENTS 



(a) LPV-3A 




FEED CONDUCTORS 



~& ^>-ANTENNA ELEMENTS 
(b) LPV-3B 




FEED CONDUCTORS 



ANTENNA ELEMENTS 



(c) LPV-3C 



Figure 7. Methods of Feed for Three Versions of LPV-3 

(In each case an end view of one pair of antenna 
elements is shown) . 



18 





Figure 8. A Close-up View of LPV-3C Showing Method of Attaching 
Elements to Feed Line. 



19 

For the half -wavelength mode the angle 4 1 for maximum gain is zero. How- 
ever, the gain does not change much in this mode for other angles. For 

maximum directivity of the V in the — - — mode, 4* ~ 32,5 ; in the — 

mode, 4* « 50°; in the 7^/2 mode, ^ ^ 52.5°. 

An experimental study was made of the effect of changing ty in an 

i o o 
LPV array. Radiation patterns for LPV-3A were measured for 4 1 = 45 , 50 , 

55 ,60 ,65 . The principal change in the radiation pattern caused by 

changing v was a change in sidelobe level when operating the LPV array in 

the higher order modes. The sidelobe levels decrease as *\> is increased. 

Data concerning the side-lobe of LPV-3A are shown in Figure 9. 

3.1.4 Radiation Pattern s and Directivity Data 

The directivity in decibels over an isotropic radiator can be computed 
approximately from the formula 

m . 41250 . . 

D = 10 log io -jwjmrr (2) 

E H 

where BW and BW are the half -power beamwidths in degrees in the E and H 
E H g 

planes, respectively. This formula ignores the effect of sidelobes on the 
directivity but is accurate to a fraction of a decibel when the sidelobes 
are more than 10 db down from the maximum. 

Plots of directivity computed from Equation 2 are shown in Figure 10 for 
LPV-3A for several values of 4 1 . The increase in directivity with higher 
mode operation is clearly seen in these data. The directivity has been 
averaged over each mode for the various 4 1 angles and the average directivity 
is plotted in Figure 1L 

Operation of the LPV arrays in the \'2 mode is similar to that of the 
LP dipole arrays. The only significant difference is a broadening of the 
beamwidths due to the reduced directivity of the half-wave dipole when 
bent to form a V, Typical E and H-plane patterns of LPV-3C in the \/2 
mode are shown in Figure 12 and for LPV-2 in Figure 13, Principal polarization 
patterns are shown with dashed lines; cross polarization with solid lines. 

As the frequency increases so that the LPV array is operated in the 
higher order modes the principal changes in the pattern are narrower 
beamwidths and the appearance of sidelobes. Typical patterns of LPV-3C 
in the higher order modes are shown in Figures 14-16. 



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Principal polar zation 
Cross polarization 



26 



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y \ 


/ ^\ 


r ^ 1 




H -PLANE 






^- — ^ 


680 


/T 1 


\ 


\ mc 


/x / 
/ x' 


\ 




/ vv 

/ V X 
/ N X 


/i 








p^259 


A. i 


\\mc 


/ \l 


Y \ 


/ i\ 

/ » X 
/ * X 

/ V X 


/ 1 \ 
/ / \ 




!■'•. Radiation patterns of f,pv-2 in \/2 mode, ty = 50 ( 
(Ci oi i polai i /.-I i i r > 1 1 nol recorded) 



27 




>^/ 


[Y^\453 




\ Xmi 


/ X I 
/ X * 


i / \ 


/ X ^ 

/ x v 


/ / \ 


/ \v 


i/ \ 


/ w 





H PLANE 



2717 
mcs. 




3010 
mcs. 





4095 
mcs. 







y — '"•■ 


"^ \ >1C" 


yT s 


N ^X *\Z)t 


/ / 




X i 


\ /k m 


/ X 


\ /\ m 


/ >\ 
/ n\ 

/ \\ 


/I \ 


/ \ X 


/ / 1 



Figure 14. Radiation patterns of LPV-3c in 3\/2 mode 
----- principal polarization 

cross polarization 






28 



E PLANE 



5866 
mcs 



6500 
mcs 




7203 
mcs 



8149 
mcs 




8622 
mcs 



H PLANE 



5866 
mcs 



6500 
mcs 



7203 
mcs 




8149 
mcs 



8622 
mcs 



Figure 15. Radiation patterns of LPV-3c in 5X./2 mode 
----- principal polarization 
cross polarization 



29 



E- PLANE 



8843 
mcs. 




12,048 
mcs. 




H- PLANE 



^W 



8843 
mcs. 




9290 
mcs, 




10,630 
mcs. 



mcs. 




12,048 
mcs. 



Figure 16. Radiation patterns of LPV-3c in 7\/2 mode 
----- Principal polarization 

Cross polarization 



30 

3.1.5 Minimum Array Length and Maximum Element Spacing 

Beyond the fact that there must be a half-wavelength element on the 
antenna at the lowest frequency, the dipole and resonant-V arrays have a 
minimum length at the lowest frequency. If the total array length does not 
exceed the length of the active region of an infinite structure with the 
same parameters at the same frequency, then the array factor will differ 
from that of the infinite structure. This is generally characterized by 
a decrease in front to back ratio as the frequency decreases below this 
critical point. 

Since the length of the active region depends upon a particularly, 
the minimum length required to reach a certain lower frequency likewise is 
a function of a. The limited amount of data concerning this dependence 
as determined from the pattern measurements is plotted in Figure 17. The 
maximum wavelength for satisfactory operation was estimated by comparing 
front to back ratio at various frequencies on the several pattern models. 
The length of the array L has been normalized with respect to the maximum 
wavelength in each case and these normalized lengths are plotted as a 
function of a in Figure 17. There is some scattering of the data due to 
a secondary dependence upon t , three different values being used in the 
data of Figure 17. The general trend as a function of a is nevertheless 
apparent and the expected longer required length for small values of a 
is illustrated. 

Satisfactory operation in the higher order modes is primarily 
contingent upon the spacing between elements, although t also seems to 
have a secondary effect. The highest frequency of operation with well- 
formed beams is shown in Table 2 for each of the LPV pattern models. 
The mode number n, designating the number of half-wavelengths of the 
mode wherein the maximum frequency is found, is also indicated a^ong 
with n times the spacing parameter o. This latter product (no) gives 
approximately the element spacing in wavelengths at the maximum frequency. 
Note that in all cases this spacing is less than three-eighth wavelength and 

m 

in several cases is approximately equal to one-quarter wavelength. 

foregoing considerations outline iimitatfons on design. They do 
necessarily provide for optimum performance accross the entire band. 
Generally ■peaking. Operation Ll improved by increasing T and decreasing O 
best performance is obtained I rom the antennas having a larger 



31 



0.8 r- 



0.7 



x 

LU 

_l 

LU 
> 





x 

< 



Q 
LU 
M 



0.6 



0.5 



0.4 



0.3 



o 

x 0.2 

O 

LU 

q: 
< 



0.0 



10 



# t = 0.95 
□ t =0.91 
x t = 0.888 




20 30 40 

c* = DEGREES 



50 



Figure 17. Minimum Length as a Function of Angle a for LPV 
Arrays 



32 



number of elements. Of the antennas tested in the pattern investigation 
LPV-3 maintained the best performance over the widest frequency band. 



LPV-1 
LPV-2 
LPV-3 
LPV-4 
LPV-5 
LPV-6 
LPV-7 
LPV-8 
LPV-9 



3.2 Impedance Measurements 







TABLE 


2 




f in 

max 


mcs 




Mod 


e No. n 


7000 








5 


5500 








5 


12000 








9 


2500 








3 


9000 








7 


11000 








9 


12000 








9 


9000 








7 


6000 








5 



no 



0.23 




0.34 




0.25 
0.34 




0.31 




0.23 




0.23 




0.37 




0.33 





The pattern models oi the LPV antennas could not be used for the measure 
of the input impedance for two reasons. First, the construction tolerances 
could not be held to as small a fraction of the wavelength as was deemed 
necessary and second, the losses and inhomogeneities of the Microdot 
feeder coax would invalidate the measured value of impedance. For these 
reasons a separate program was undertaken to measure the input impedance 
of the LPV arrays for as many values of the parameters as was practical, 
in order to compile data which could be used as a basis for the design 
of LPV antennas. In addition, correlation between the pattern and impedance 
data was sought. 

3.2.1 Construction of the Impedance Models 

Since the radiation properties of the LPV-3A were the best of all 
pattern models up to the time at which the impedance program was initiated, 
it was decided to use the LPV-3A design for the impedance model. (In 
LPV-.1A th« elements and their respective conductor are coplanar) . ILPV-3A 
la shown in Figure LS. The impedance model is scaled up from LPV-3A by a 
faotOX Oi 2.8 I, the 0.410 inch diameter of the feeder permits the use 

' ... i Low loss, tel ion dielectric coaxial cable for the feed coax. 
Preliminary mea^ its showed thai I h<- small loss in the length of 



33 




Figure 18. Model ILPV-3 Used for Impedance Measurements. 



34 



cable could be neglected in the measurement of standing wave ratios of 
4:1 or less. The feeder and elements were made of coin silver tubing. The 
half length, h, of the largest element is 16.8 inches and the smallest, 4.9 
inches. The element diameter was held constant at 0.140 inches, which means 
that the h/a ratio varies from 80 to 240. The length of the section of 
feeder along which the elements are attached is 25.5 inches. An additional 
8.4 inches of feeder beyond the largest element is terminated in a short 
circuit to eliminate the possibility of end effect current interfering 
with the measuring equipment. The value of t is 0.95 and a is 0.0266. 4» 
angles of 40°, 45°, 50°, and 55° were obtained by bending the elements which 
are silver-soldered onto the feeders. Built into this model was a provision 
for easily adjusting this characteristic impedance of the feeder, Z q , to value! 
of 75,100,125, or 150 ohms. The accuracy was least for the 150 ohm value 
because of the error incurred due to the larger gap at the feed point. 
It can be seen that ILPV-3A, with its superior feed coax, eliminates 
the objections to the use of the pattern models for impedance measurements. 

3.2. 2 Description of the Measurements and the Measuring Equipment 
The input impedance was measured as a function of frequency every 
half-period according to the formula 

f = f T" n/2 4 n = 0, 1, 2, . 

rv 2 o 

The frequencies covered were from f = 161.2 mcs to f g3 = 3882 mcs. In 
order to cover this wide frequency range (24:1) two different measuring 
devices were used. Below 640 mcs the impedance measuring device was the PRD 
type 219 standing wave indicator which measures the reflection coefficient 
by means of a crystal-and-probe assembly which is rotatable in a calibrated 
drum, corresponding to the movement of the conventional probe in a slotted 
line. Above 640 mcs, a Hewlett-Packard model 805-A slotted line was used 
to measure the standing wave ratio and position of voltage minimum. Several 
oscillators were used to cover the frequency range. A heterodyne 
frequency Mt«r assured repetition of the various frequencies. A picture 
of lance set up Is shown in Figure 19. Note that the antenna and 
all •■', i on a bench equipped with casters. During the 

performance of any set oi measurements, the whole set up is rolled to a 



35 




Figure 19, Impedance Measuring Set-up 



36 



specially constructed window in the wall of the antenna laboratory, which 
is on the second floor of the building. Thus the measurements are performed 
on the inside while the antenna is looking into an uncluttered environment. 
The impedance measuring set up is shown schematically in Figure 20. It is 
essential to use a low pass filter as indicated in the diagram, because 
satisfactory operation of the PRD Standing Wave Indicator as well as the 
slotted line requires a strictly monochromatic signal. In each measurement 
the impedance is referred to the input terminals at the front of the antenna. 
The reference used in the null shift method was determined by a measurement 
of the short circuited feedpoint as a function of frequency through the 
37 inches of RG-U5A coaxial cable. 

3.2.3 General Results of the Measurements of Imp edance on LP Structures 
The results of the impedance measurements can be analyzed by comparing 
them with the impedance characteristics of the LP dipole array. In the 
LPDA the impedance is an almost periodic function of the logarithm frequency, 
the period being log T. The slight deviation from periodicity is due to 
the necessary truncation at the front of the antenna. This front truncation 
means that the section of feeder from the feed point out to the "active" 
region is not scaled exactly with frequency, resulting in an impedance 
transformation which is a function of frequency, causing a 
translation of the impedance locus. The input impedance of the LPDA is 
predominately real and is centered at 55 to 100 ohms. The SWR measured in 
practice varies from 1.3:1 to 2:1 when using the center resistance value R q 

as a reference for the SWR. R is determined by drawing a circle which 

o 
encloses the locus of the measured impedances on a Smith chart. The 

circle is centered on the resistance axis, and the value of R q is given by 



R = \ R R . (3) 

o V max min v ' 

where R and R are respectively the maximum resistance and the minimum 

max mln 
resistance given by the intersection of the circle with the resistance axis. 

maximum standing wave ratio wi th re spect to R q is given by 

VSWR = / -^— < 4 > 

min 




37 



t3 

I 
■P 

0) 
CO 

c 

■H 

Sh 
3 
cfi 
rci 
0) 



O 

c 



o 






o 

o 

1—1 

CQ 



o 

CM 

<D 

U 
3 
bo 

•H 



38 



3.2.4 Input Impedance: Single Mode Operation 

Considering any one mode of operation, one finds that the impedance 
characteristic of the LPVA is comparable with that of the LPDA. The 
impedance within a given mode is predominately real, clustered about some R q . 
Figure 2Kb) shows the maximum SWR which may be expected in any one mode, 
referred to the R of that mode. The maximum SWR varies from 1.4 to 1.8 
and is not strongly dependent on the feeder characteristic impedance Z q . 
Figure 21(a) shows a plot of the center resistance value R q for the various 
LFV modes vs. the characteristic impedance of the feeder. It shows that the 
center value R for each mode increases with Z q in a non-linear fashion. 
This behavior is also demonstrated in the LPDA. Thus control of the impedance 
level can be accomplished by controlling the feeder characteristic impedance. 
In Figure 21 the 4> angle was held at 50°; similar variations were obtained 
with 4> angles from 40 to 55 . 

3.2.5 Input Impedance: Multi-Mode Operation 

Figure 22 illustrates the impedance variation over the whole range of 
frequencies. Since any attempt to draw a line connecting all the measured 
points would lead to a complicated graph, the impedance locus is plotted 
as follows: All points which lie in a given mode are enclosed by a circle 
which represents the maximum SWR of each mode. In Figure 22 the four modes 
shown are the V», 3ty2, 5^/2, and l\/1. As the transition range is entered, 
that is, for frequencies in which the operation changes from one mode to 
another, the impedance locus departs from one of the mode circles and 
rapidly swings out and around the Smith chart, until the next mode circle 
is entered. The frequencies noted on the chart are the entrance and exit 
frequencies for each mode, in addition to a few frequencies in the transition 
region. For this Figure 4* is 50° and Z q is 100 ohms. Their values were 
chosen because they are representative of the data which have been recorded 
to date. 

3,2.5.1 Deti rmination of the Weighted Mean Resistance Level R^ 
If it is d to operate over the several modes, a compromise must be 
made to determine a fixed input impedance level. This level may be fixed by 
external consld<r;ii ions such as the desirability of using certain coaxial 
feed lines or the necessity of matching source or receiver impedance. 



39 




60 80 100 120 140 

Z OF FEEDER , OHMS 



160 



Figure 21. Resistance Level R and SWR with Respect to R 

o o 

for Each Mode vs. Characteristic Impedance of 
Feeder for ^ = 50 . 



4( 




Figure- 22. Impedance Plot 



41 



However for the purpose of the displaj of data herein a resistance which 

is called the weighted mean resistance Level R na^ been selected 

WM >-cu„ 

\ M ls determined by the collection of measured points in the \ 2 and 
3N 2 mode from this requirement;; [x ls desired that the maximum standing 
rove ratio *itfi respect to r^ fo , botn the \ 2 and 3 x 2 modeg be equai 
Thus the expressions lor standing *au ratio m terms rf the maximum and 
minimum resistance values as read from the two mode circles (from a plot 
similar to Figure 22) are equated„ Accordingly 

1 r I P I 

WM 1/2 L"- I .. "T" 5 J 



1 2 



fcerejp j >2 |ia the maximum magnitude of the reflection coefficient in the 



- mode *ith Respect to 



kV) a3 tne ClrnTer ° T ne maximum magnitude of p 

1 <i 



is given by the hyperbolic distance between R WM and the minimum resistance 

level encountered in the-- mode the minimum Level is R /sWR 

o 1 2 / 1 2° 
The fraction subscripts indicate the mode). Therefore 

P 



L i 



R o 1 2/ SWR l 2 



' WM 



P 



o L 2 



r SWR ^Tr- 
1 2 WM 



(6) 



Trie maximum magnitude ,1 p ^ . Ls given by the hyperbolic distance between 

V and the - m £?i^ ,r ' resistance Level encountered in the 3/2 mode, the maximum 

-evei Ls R SWR r> Thus 
o J, <s 3 2 



P 



3 2 



- 


R 
o 3, 2 




R WM 


o 3 2 


SWR 3 2 


R 

- WM 



Hence 



I J 



SWR 



WV) 3 '2 i 



3 2 
>3 2 



(7) 



(8) 



I reason for cl s ag the minimum Level in the 1/2 mode and the maximum 
L evel in the 3. 2 mode Ls tnat m every case measured so far 



R 



3 i 2 



\ 



M 



> 3 2 



quating (5) and (8) using (6) and (7) with the condition (9) *e can 



olve for R^ and find thai 



42 



L R %* (10) 

*WM " \l o 1/2 o 3/2 SWR 1/2 

Thus R^ differs from the geometric mean /R q 1/2 R q 3/2 ~ °y a weighting factor 
which ^kes into account the relative difference which may exist between the 
maximum standing wave ratios which occur in each mode. 
3.2.5.2 B. as a Function of LPVA Parameters 

Figure 23 shows a graph of R^ vs Z q of the feeder for several values 
of ^. Note the nearly linear relationship between R^ and Z q , and also note 
the insensitivity to 4> in the region where Z q = 100 ohms. Using the data of 
Figure 23 a graph can now be plotted which shows how the standing wave ratio 
with respect to R^ varies over the band. See Figure 24. A Z q of 100 A and 
a ^ of 50° were again chosen as representative. The transition regions are 
marked by an increase in the standing wave ratio and are clearly evident in 
Figure 24. The standing wave ratio is below 2:1 for all but the lowest mode, 
in which there are a few points above 3:1. It can be seen that this antenna 
would provide a fair match to 80 ohms over the four modes. 

Table 3 is a condensation of the important features of a series of 
graphs similar to Figure 24. Tabulated is the average SWR for each mode with 
respect to R^ for various values of Z q and Y . 



43 



120 



110 



100 



c/> 

X 

o 



90 



o?80 



70 



60 



50 



40 



— 












<|/=45° 


— 












* : 


= 40° 


— 












ySir- 


50° 


— 












^r-i 


>5°,* 


— 
















— 
















































" 




_L 


_L 


L 


i 


j_ 


1 



75 85 95 105 115 125 

Z OF FEEDER, OHMS 



135 145 



Figure 23. Weighted Mean Resistance Level R vs. Characteristic 

WM 

Impedance of Feeder Z for Various + Angles. 



44 











CO 










o 










B . 


>. 







I) 


s< 


o 


o 




J3 


01 O 


c 


m 




•»-> 


■H 00 


CO 

3 


ii 


4 


o 


in 

QJ II 


cr 




o 


Ih 


CO u 


^»- 


o 






U 




^H 




c ■ 


<H <H 






•a 


a a: 






II 


CO 


CO 




n 




N 


E 


CO 


i 


o 


•H 




> 


> 


S) 


_< 


•o -C 




u. 




« 


CO 


£ 


J 




E 


•»■> > 


l-t 




fc. 


x; co 


CO 









M -H 




o 
o 
o 

8 

o 

IO 

O 
O 
O 

CO 

8 



o 
o 
o 



8 



o 
o 

IO 



s 

O 
O 
ro 



O 
O 
CJ 

O 
IO 



(0 
O 

2 

>-" 

o 

z 

UJ 

Z) 

o 

UJ 



CO 

UJ 
(T 

D 
O 



TABLE 3 
TaoLt ot \ a lues ot average SWR > ; ' h 
rt-ptct to R w for different Z and 4*, 



45 



4< 


Z 
o 


R 

WM 




Ave k ag 


e SWR wrt F 


l WM 




2 


3^ 
2 


5* 
2 


7^ 

2 " 


40° 


?5 


58„2 


L.6 


1.5 


1.6 


1.6 




iOO 


32. 


I .8 


-.4 


L.5 


i,6 




125 


9Qo5 


2„3 


1.5 


1.5 


1.6 




150 


£.0. 


2. 


i»7 


2,3 


?. 


45° 


75 


54„ 


1,8 


1 D 8 


L.8 


2„ 




100 


79 . 4 


L.6 


L.6 


L.7 


L.7 




125 


i04 o 


2.4 


I = 5 


L.4 


L.8 




150 


i24„8 


2.2 


«. o »-< 


1.6 


1.8 


50° 


?5 


65. 


L.9 


[ , 6 


L.5 


I .5 




100 


80 


io9 


1 ,6 


1.6 


i,6 




125 


90, 


L„9 


i . 5 


1,6 


lo 6 




l50 


115o 


2, 


1.6 


1.7 


2 2 


55° 


75 


53.5 


2 3 


1 8 


1 .8 


2 




100 


69 o 3 


2 4 


1 7 


1 7 


1 8 




i25 


81. 


2 


1 6 


1 6 


2 




150 


94,7 


2 3 


2 5 


2 


2 3 



46 

4. DESIGN CONSIDERATIONS FOR PARTICULAR APPLICATIONS 

Several additional features of log-periodic dipole and V arrays have 
been briefly investigated as being of interest in some specialized applications. 

4.1. Elimination of Central Elements 

It is apparent from the preceding data that the resonant-V array is 
appropriate for use when it is desired to cover a number of discrete frequency 
bands which are widely distributed over the spectrum. Such frequency allocation 
are used in a number of commercial and government services. However, 
it is not often possible to fit the desired bands with a resonant-V array 
without some modification. One useful modification which has been 
proved feasible by measurement involves the elimination of some central 
elements from either the LP dipole or LPV array. 

Since the coverage of any small frequency band is obtained from relatively 
few of the elements on the array, coverage of several adjacent bands may be 
obtained by retaining only the elements which are in the active region for 
those particular bands. Elements which on the ordinary dipole or V-array 
would contribute to the coverage of undesired portions of the spectrum 
can be simply removed and the remaining elements pushed together to shorten 
the over-all length of the array. 

When using the resonant V array in higher modes, it is necessary to keep 
in mind tnat the elimination of central elements which may not be 
necessary in the V2 mode will also introduce holes in the coverage on the 
higher modes. Figure 25 shows a photograph of a pattern model LPV array 
designed to cover several bands with some central elements eliminated. 
26 shows the correspondence between elements on the antenna and 
bands covered. 






\ . . <- I',- 

pies of array design which have previously been applied to 
3 
■•ts can also be app] Led to arrays of LPV elements 

achieve « Although further investigations of LPV elements 

"i phase center mui methoda of feed ^re needed 

i vantage of using LP resoriant-V 's as 

-. has been postulated and verified by a few measurement 






47 




Figure 25. An LPV Array Showing Elimination of Central Elements 
to Tailor Design to Coverage of Desired Bands. 



48 



to 




I 

CO 

a 



CO 

< 

c 
d 

e 

CO 
0) 

K 

>> 
h 

> -c 

O I 
■ 

m e 
•o -h 

c £ 

03 r-l 



V 

u 

3 
bo 



49 

In order to maintain frequency independent performance in an array of 
LP elements,, the phase centers of the elements should remain at a constant 
distance apart in terms of the wavelength. This is readily accomplished 
by feeding the LP elements from a common point as shown in Figure 27. With 
this method of feed, however, the direction of the axes of the several 
elements will vary. Using conventional end -fire elements therefore 
produces different element patterns because of the shift of the end-fire 
direction from element to element (see Figure 27). 

In order to achieve maximum directive gain for an array of LP elements 
all of the elements of the array should have maximum directive gain in the 
same direction. Hence, the beam of each element should be tilted off-axis 
by the proper amount Such a beam tilt can be achieved by simply tilting 
the elements relative to the feeder„ Tilts in the E plane are produced in 
either the dipole array or the resonant -V array when the elements are 
aligned relative to the feeder as shown in Figure 28 Furthermore, a tilt 
in the H-plane can be achieved in the v array by tilting the elements as 
shown in Figure 29, In each of these cases the tilt of the beam is achieved 
by tilting the element pattern The principal pattern characteristics are 
determined by the array factor and, aside from the pattern tilt, the patterns 
remain essentially the same as for the array with until ted elements. 

The results of a few measurements ox beam tilt are shown in Figures 30 
and 31. In these curves the beam tilt was calculated by taking the aver- 
age of the angles of the half -power points to locate the beam maximum. The 
deviation of this angle from the array axis of LPV-11 is plotted for several 
angles of tilt in Figure 30 Similar data for the H-plane are shown in Figure 
31. The beam tilt is more pronounced in antennas with fairly large a since 
the element pattern in such cases is relatively more important in determining 
beam shape. 

The beam tilt is not realized to a very great degree in the \/2 mode 
since the elements themselves are not highly directive in this mode. A con- 
sistent beam tilt is observed in the higher modes and the data for these 
modes are shown in Figures 30 and 31. 



50 



ELEMENT 
PATTERN OF 
ELEMENT no. 5 



FEED REGION 




ELEMENT PATTERN 
OF ELEMENT no.l 



LP ELEMENTS 



Figure 27. A Frequency Independent Array of 
Log-Periodic Elements. 
















51 



(a) 

LP DIPOLE ARRAY WITH ELEMENTS 
TILTED IN E - PLANE 




LPV ARRAY WITH ELEMENTS 
TILTED IN E - PLANE 



Figure 28. Method of Tilting Elements in Dipole and 
V Arrays to Achieve Beam Tilt in E Plane, 



52 



V ELEMENTS 




FEEDER 



Figure 29. Method of Tilting Elements in V Array 
to Achieve Beam Tilt in H Plane 



53 



m 

= <*\ ° 

i d d 
> » H 

Q. m b 



CO 



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txl 
UJ 

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UJ O 



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Ul 



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cotr 

UIO 

ujui 
tro 

iu>- 

z 
z!£ 

Ul> 



I 



sin 




<"--. 



CO 
UJ 

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o 

z 

Ul 

o 

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cr 
ti- 



ro 



CVJ 



8 



m o ■*> O 

"S33d93G Nl 1111 INV38 



in 



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cr 

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54 



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55 

5. CONCLUSIONS 

It is obvious that a complete parameter study of the LPV arrays has 
not yet been accomplished. In any experimental investigation of wide band 
antennas one is confronted with the task of making thousands of measurements. 
The data reported here are drawn from hundreds of radiation patterns and 
over two thousand; impedance measurements. Effort is now being directed 
towards making the experimental study by using a digital computer rather than 
laboratory models. 

Enough data have been presented, however, to demonstrate the feasibility 
of the ideas expressed, to illustrate the validity of the general theory of 
operation, and to provide some data for practical designs. An important 
observation from the design viewpoint is the fact that the input impedance 
depends primarily upon the impedance of the feeder whereas the pattern 
depends primarily upon ~r, 0, and 4 1 . This enables one to exercise somewhat 
independent control over the impedance and pattern over a limited range of 
parameters. 

The LP resonant-V array provides essentially frequency-independent 
coverage of each of several frequency bands. In multi-mode operation, the 
characteristics change in a desirable way with frequency, achieving higher 
directive gain from the same physical structure as frequency increases. 
Antennas designed according to these concepts should find application whenever 
coverage of several widely dispersed frequency bands is desired. 



56 

REFERENCES 



1. J„ D. Dyson, "The Equiangular Spiral Antenna," IRE Trans, on Antennas 
and Propagation, Vol. AP-7, pp. 181-187, April, 1959. Technical Report 
No. 21, Contract No. AF 33(616)-3220, Antenna Lab., University of 
Illinois, Urbana, Illinois, September 1957. 

2. J. D. Dyson, "The Unidirectional Equiangular Spiral Antenna," IRE. 
Trans. , Vol. AP-7, October, 1959, pp. 329-334. Technical Report No. 
33, Contract No. AF 33 (616) -322,0, Antenna Lab., University of Illinois, 
Urbana, Illinois, July 1958. 

3. R. H. DuHamel & D. G. Berry, "Logarithmically Periodic Antenna Arrays," 
1958 IRE Wescon Convention Records , Pt . I, pp. 161-174. 

4. R. H, DuHamel & F. R. Ore, "Log-Periodic Feeds for Lens and Reflectors," 
1959, IRE National Convention Record, Pt . I, pp. 128-137. 

5. D, E. Isbell, "Log-Periodic Dipole Arrays," Technical Report No. 39, 
Contract No. AF 33(616)-6079, Antenna Lab., University of Illinois, 
Urbana, Illinois, June 1959. IRE Trans, on Antennas and Propagation , 
Vol. AP-8, pp. 260-267, May 1960~ 

6. J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York, N. Y. 
1941, p. 488. 

7. S. A. Schelkunoff & H. T. Friis, Antennas, Theory and Practice, 
John Wiley, New York, N. Y., 1952, p. 502. 

8. J. D„ Kraus, Antennas , McGraw-Hill, New York, N. Y., 1950, p. 25. 



ANTENNA LABORATORY 
TECHNICAL REPORTS AND MEMORANDA ISSUED 



Contract AF33 (616) -310 

"Synthesis of Aperture Antennas/' Technical Report No. 1, C.T.A. Johnk 
October, 1954.* 

"A Synthesis Method for Broad-band Antenna Impedance Matching Networks " 
Technical Report No. 2, Nicholas Yaru, 1 February 1955.* 

? The Asymmetrically Excited Spherical Antenna/' Technical Report No. 3, 
Robert C. Hansen, 30 April 1955.* 

"Analysis of an Airborne Homing System/' Technical Report No. 4, Paul E. 
Mayes, 1 June 1955 (CONFIDENTIAL). 

"Coupling of Antenna Elements to a Circular Surface Waveguide/' Technical 
Report No. 5, H. E. King and R. H. DuHamel, 30 June 1955.* 

"Axially Excited Surface Wave Antennas/' Technical Report No. 7, D. E. Royal, 
10 October 1955.* 

"Homing Antennas for the F-86F Aircraft (450-2500mc)/' Technical Report No. 8, 
P.E. Mayes, R.F. Hyneman, and R.C. Becker, 20 February 1957, (CONFIDENTIAL). 

"Ground Screen Pattern Range," Te chnical Memorandum No. 1, Roger R. Trapp, 
10 July 1955.* 



Contract AF33 (616) -3220 

"Effective Permeability of Spheroidal Shells," Technical Report No. 9, E. J. 
Scott and R. H, DuHamel, 16 April 1956. 

"An Analytical Study of Spaced Loop ADF Antenna Systems," Technical Report 
No. 10, D. G. Berry and J. B. Kreer, 10 May 1956. 

"A Technique for Controlling the Radiation from Dielectric Rod Waveguides," 
Technic al Report No. 11, J. W. Duncan and R. H. DuHamel, 15 July 1956. 

"Directional Characteristics of a U-Shaped Slot Antenna," Technical Report 
No. 12, Richard C. Becker, 30 September 1956.* 

"impedance of Ferrite Loop Antennas," Technical Report No. 13, V. H. Rumsey 
and W. L, Weeks, 15 October 1956. 

"Closely Spaced Transverse Slots in Rectangular Waveguide," Technical Report 
No, 14, Richard F. Hyneman, 20 December 1956. 









"Distributed Coupling to Surface Wave Antennas " Technical Report No. 15 
Ralph Richard Hodges, Jr . 5 January 1957. 

"The Characteristic Impedance of the Fin Antenna of Infinite Lengthy" Technical 
Report No, 16 , Robert L. Carrel, 15 January 1957.* 

"On the Estimation of Ferrite Loop Antenna Impedance, " Technical Report No. 17, 
Walter L. Weeks, 10 April 1957.* 

"A Note Concerning a Mechanical Scanning System for a Flush Mounted Line Source 
Antenna/' Technical Report No. 18, Walter L. Weeks, 20 April 1957. 

'Broadband Logarithmically Periodic Antenna Structures,' Technical Report No. 19, 
R. H. DuHamel and D. E. Isbell, 1 May 1957. 

"Frequency Independent Antennas," Technical Report No. 20, V. H. Rumsey, 25 
October 1957. 

"The Equiangular Spiral Antenna," Technical Report No. 21, J. D. Dyson, 15 
September 1957. 

"Experimental Investigation of the Conical Spiral Antenna," Technical Report 
No. 22, R. L. Carrel, 25 May 1957.** 

"Coupling between a Parallel Plate Waveguide and a Surface Waveguide," Technical 
Report No. 23, E. J. Scott, 10 August 1957. 

"Launching Efficiency of Wires and Slots for a Dielectric Rod Waveguide," 
Technical Report No. 24, J. W. Duncan and R. H. DuHamel, August 1957. 

'The Characteristic Impedance of an Infinite Biconical Antenna of Arbitrary 
Cross Section," Technical Report No. 25, Robert L. Carrel, August 1957. 

"Cavity-Backed Slot Antennas," Technical Report No. 26, R. J. Tector, 30 
October 1957. 

"Coupled Waveguide Excitation of Traveling Wave Slot Antennas," Technical 
Report No. 27, W. L. Weeks, 1 December 1957. 

"Phase Velocities in Rectangular Waveguide Partially Filled with Dielectric," 
Technical Report No. 28, W. L. Weeks, 20 December 1957. 

Measuring the Capacitance per Unit Length of Biconical Structures of Arbitrary 
Section," Technical Report No. 29, J. D. Dyson, 10 January 1958. 

-Planar Logarithmically Periodic Antenna Structure," Technical Report No. 30 , 
II, 20 February 1958. 

I m Rectangular Slots," Technical Report No. 31, N. J. 
Kuhr- .10 March I !;. r .H 

I Ltation ol a Surface Wave on a Dielectric Cylinder," 
Techl port No. 32, J, W. Duncan, 25 May 1958. 



"A Unidirectional Equiangular Spiral Antenna/' Technical Report No. 33, J. D. 
Dyson, 10 July 1958 „ 

"Dielectric Coated Spheroidal Radiators/' Technical Report No. 34, W. L. Weeks 
12 September 1958. 

"A Theoretical Study of the Equiangular Spiral Antenna." Technical Report 
No. 35, P. E. Mast, 12 September 1958. 

Contract AF33 (616) -6079 

"Use of Coupled Waveguides in a Traveling Wave Scanning Antenna/' Technical 
Report No. 36, R. H. MacPhie, 30 April 1959. 

"On the Solution of a Class of Wiener-Hopf Integral Equations in Finite and 
Infinite Ranges/' Technical Report No. 37, Raj Mittra, 15 May 1959. 

"Prolate Spheroidal Wave Functions for Electromagnetic Theory/' Technical 
Report No. 38, W. L. Weeks, 5 June 1959. 

"Log Periodic Dipole Arrays," Technical Report No. 39, D.E. Isbell, 1 June 1959. 

"A Study of the Coma-Corrected Zoned Mirror by Diffraction Theory " Technical 
Report No. 40, S. Dasgupta and Y. T. Lo, 17 July 1959. 

"The Radiation Pattern of a Dipole on a Finite Dielectric Sheet," Technical 
Report No. 41 , K. G, Balmain, 1 August 1959. 

"The Finite Range Wiener-Hopf Integral Equation and a Boundary Value Problem 
in a Waveguide," Technical Report No. 42, Raj Mittra, 1 October 1959. 

"impedance Properties of Complementary Mul titerminal Planar Structures," 
Technical Report No. 43, G. A. Deschamps, 11 November 1959. 

"On the Synthesis of Strip Sources," Technical Report No. 44, Raj Mittra, 
4 December 1959. 

"Numerical Analysis of the Eigenvalue Problem of Waves in Cylindrical Waveguides, 
Technical Report No. 45, C. H. Tang and Y. T. Lo, 11 March 1960. 

"New Circularly Polarized Frequency Independent Antennas With Conical Beam or 
Omnidirectional Patterns," Technical Report No. 46, J.D.Dyson and P.E. Mayes, 
20 June 1960. 

"Logarithmically Periodic Resonant-V Arrays," Technical Report No. 47, P.E. 
Mayes and R. L. Carrel, 15 July 1960. 



* Copies available for a three week loan period, 
** Copies no longer available. 



AF 33(616) -6079 



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Chance-Vought Aircraft Division 

United Aircraft Corporation 
Attn: R.C. Blaylock 
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M/F Contract NOa(s) 57-187 

Dallas, Texas 

Collins Radio Company 

Attn: Dr. R. H. DuHamel 

M/F Contract AF33(600)-37559 
Cedar Rapids, Iowa 



Dome & Margolin, Inc. 

M/F Contract AF33(600)-35992 

30 Sylvester Street 

Westbury 

Long Island, New York 

Douglas Aircraft Co., Inc. 
Attn: G. O'Rilley 

M/F Contract AF33(600)-25669 & 
AF33(600)-28368 
Tulsa, Oklahoma 

Exchange and Gift Division 
The Library of Congress 



Washington 25, D.C. 



(2 copies) 



Fairchild Engine & Airplane Corp. 
Fairchild Aircraft Division 
Attn: Engineering Library 

S. Rolfe Gregory 

M/F Contract AF33(038)-18499 
Hagerstown, Maryland 



CONVAIR 

Attn: R. Honer 

M/F Contract AF33(600)-26530 
San Diego Division 
San Diego 12, California 



Dr . Frank Fu Fang 

Boeing Airplane Company 

Transport Division, Physical Research 

Renton, Washington 



General Electric Company 

Attn: D. H. Kuhn, Electronics Lab. 
M/F Contract AF30(635)-12720 
Building 3, Room 301 



CONVAIR 

Fort Worth Division 

Attn: C. R. Curnutt 

M/F Contract AF33(600)-32841 & College Park 

AF33(600)-31625 113 S. Salina Street 
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Department of Electrical Engineering 

Attn: Dr. H. G. Booker 
Cornell University 
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University of Denver 
Denver Research Institute 
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Dalmo Victor Company 

Attn: Engineering Technical Library 
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General Electronic Laboratories, Inc. 
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Goodyear Aircraft Corporation 
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M/F Contract AF33(616)-5017 
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Granger Associates 
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AF 33(616)-6079 



Grumman Aircraft Engineering Corp. 
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M/F Contract AF33(616)-5120 
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Gulton Industries, Inc. 
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M/F Contract AF33(600)-36869 
P„0, Box 8345 
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Hallicraf ters Corporation 
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M/F Contract AF33(604)-21260 
440 W. Fifth Avenue 
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Technical Reports Collection 
Attn: Mrs, E. L. Hufschmidt 
Librarian 
303 A. Pierce Hall 
Harvard University 
Cambridge 38, Massachusetts 

Hoffman Laboratories, Inc. 

Attn: S. Varian (for Classified) 
Technical Library (for 

Unclassified) 
M/F Contract AF33(604)-17231 
Los Angeles, California 

Dr. R. F. Hyneman 

P.O. Box 2097 

Mail Station C-152 

Building 600 

Hughes Ground Systems Group 

Fullerton, California 



ITT Laboratories 
Attn: L. DeRosa 

M/F Contract AF33(616)-5120 
500 Washington Avenue 
Nutley 10, New Jersey 



Corp 



Giffin, ECM Lab, 



ITT Laboratories 

A Div. of Int. Tel. & Tel 

Attn: G. S 
3700 E. Pontiac Street 
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Jansky and Bailey, Inc. 
Engineering Building 

Attn: Mr. D. C. Ports 
1339 Wisconsin Avenue, N.W, 
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Jasik Laboratories, Inc. 
100 Shames Drive 
Westbury, New York 



John Hopkins University 
Radiation Laboratory 
Attn: Librarian 

M/F Contract AF33(616)-68 
1315 St. Paul Street 
Baltimore 2, Maryland 

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Johns Hopkins University 
8621 Georgia Avenue 
Silver Spring, Maryland 



HRB-Singer, Inc. 

Attn Mr. R. A. Evans 
Science Park 
State College, Pa. 

Dwight I shell 
■1020 Sunnyslde 
Seal i 1 e 3, Washington 



Lincoln Laboratories 
Attn: Document Room 

M/F Contract AF19(122)-458 
Massachusetts Institute of Technology 
P.O. Box 73 
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AF 33(616)-6079 



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M/F Contract AF33( 600)-37292 
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University of Michigan 
Aeronautical Research Center 
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Lockheed Missiles & Space Division 
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M/F Contract AF33(600)-37705 
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Baltimore 3, Maryland 

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McDonnell Aircraft 

P.O. Box 516 

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St. Louis 21, Missouri 

Melpar, Inc. 

Attn: Technical Library 

M/F Contract AF19( 604) -4988 
Antenna Laboratory 
3000 Arlington Blvd. 
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Melville Laboratories 
Walt Whitman Road 
Melville, Long Island, 
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Motorola, Inc. 

Attn: R. C. Huntington 
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Physical Science Lab. 

Attn; R. Dressel 
New Mexico College of A and MA 
State College, New Mexico 

North American Aviation, Inc. 

Attn: J. D. Leonard, Eng. Dept . 
M/F Contract NOa(s) 54-323 
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Attn: H. A. Storms 

M/F Contract AF33(600)-36599 
Department 56 
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Hawthorne, California 

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Microwave Laboratory 
Northwestern University 
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AF 33(616)-6079 



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Microwave Research Institute 
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Melbourne, Florida 

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AF 33(616)-6079 



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Sylvania Electric Products, Inc. 

Electronic Systems Division 

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Mountain View, California 

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M/F Contract AF33(038)-21250 
100 First Street 
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University of Texas 
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Development Engineering 
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Friendship Airport 
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New York University 

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New York 3, New York 

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Government Engineering College 

Jabalpur, M.P. 

India 

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10829 Berkshire 
Westchester, Illinois 

The Engineering Library 
Princeton University 
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Indian Institute of Technology 
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India 

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